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MELVILLE, N.Y. — Dzhokhar Tsarnaev left a “deathbed” note scrawled inside the hull of the boat in which he was captured, claiming he and his older brother set off bombs at the Boston Marathon as retribution for America’s attacks on Muslims in Iraq and Afghanistan, a law enforcement source said Thursday.

The note said the victims of the April 15 attack — three dead and more than 260 injured — were essentially collateral damage, the source said.

Investigators believe a badly wounded Tsarnaev, 19, thought he was dying when he scrawled it, the source said. “He seemed to consider it a type of deathbed letter,” the source said.

The source said the note was stronger evidence against Tsarnaev than similar statements he made to the FBI in his hospital room. Those statements were made before he was advised of his rights and could be ruled inadmissible as evidence at a trial, the source said.

The boat was seized by the FBI after the manhunt and the part of the boat wall containing the note will be removed for preservation and analysis, the source said. The wall was badly damaged by bullets fired by police in Watertown, Mass.

His older brother, and suspected bombing accomplice, Tamerlan Tsarnaev, 26, died following a gun battle with police. Authorities captured Dzhokhar Tsarnaev after a massive manhunt following his escape from the same encounter.

In the note, Tsarnaev also referred to his brother as a martyr who he wouldn’t miss because he would soon be joining him in the afterlife, the source said.

Tamerlan Tsarnaev was killed in a shootout with police four days after the marathon bombings; his brother was later found hiding in a boat in a suburban backyard and is being held on federal terror charges.